Evolving Scale-Free Networks by Poisson Process: Modeling and Degree Distribution

Complex Network Evolution Model Based on Turing Pattern Dynamics

Complex network models are helpful to explain the evolution rules of network structures, and also are the foundations of understanding and controlling complex networks. The existing studies (e.g., scale-free model, small-world model) are insufficient to uncover the internal mechanisms of the emergence and evolution of communities in networks. To overcome the above limitation, in consideration of the fact that a network can be regarded as a pattern composed of communities, we introduce Turing pattern dynamic as theory support to construct the network evolution model. Specifically, we develop a Reaction-Diffusion model according to Q-Learning technology (RDQL), in which each node regarded as an intelligent agent makes a behavior choice to update its relationships, based on the utility and behavioral strategy at every time step. Extensive experiments indicate that our model not only reveals how communities form and evolve, but also can generate networks with the properties of scale-free, small-world and assortativity. The effectiveness of the RDQL model has also been verified by its application in real networks. Furthermore, the depth analysis of the RDQL model provides a conclusion that the proportion of exploration and exploitation behaviors of nodes is the only factor affecting the formation of communities. The proposed RDQL model has potential to be the basic theoretical tool for studying network stability and dynamics.

Limited resource network modeling and its opinion diffusion dynamics

The preferential attachment of the Barabási-Albert model has been playing an important role in modeling practical complex networks. The preferential attachment mechanism describes the role of many real systems, which follows the characteristic "the rich get richer." However, there are some situations that are ignored by the preferential attachment mechanism, one of which is the existence of the limited resource. Vertices with the largest degree may not obtain new edges by the highest probability due to various factors, e.g., in social relationship networks, vertices with quite a lot of relationships may not connect to new vertices since their energy and resource are limited. Hence, the limit for degree growing is proposed in our new network model. We adjust the attachment rule in light of the population growth curve in biology, which considers both attraction and restriction of the degree. In addition, the unaware-aware-unaware opinion diffusion is studied on our proposed network. The celebrity effect is taken into consideration in the opinion diffusion process.

Dynamic Immunization Node Model for Complex Networks Based on Community Structure and Threshold

In the information age of big data, and increasingly large and complex networks, there is a growing challenge of understanding how best to restrain the spread of harmful information, for example, a computer virus. Establishing models of propagation and node immunity are important parts of this problem. In this article, a dynamic node immune model, based on the community structure and threshold (NICT), is proposed. First, a network model is established, which regards nodes carrying harmful information as new nodes in the network. The method of establishing the edge between the new node and the original node can be changed according to the needs of different networks. The propagation probability between nodes is determined by using community structure information and a similarity function between nodes. Second, an improved immune gain, based on the propagation probability of the community structure and node similarity, is proposed. The improved immune gain value is calculated for neighbors of the infected node at each time step, and the node is immunized according to the hand-coded parameter: immune threshold. This can effectively prevent invalid or insufficient immunization at each time step. Finally, an evaluation index, considering both the number of immune nodes and the number of infected nodes at each time step, is proposed. The immune effect of nodes can be evaluated more effectively. The results of network immunization experiments, on eight real networks, suggest that the proposed method can deliver better network immunization than several other well-known methods from the literature.

Evolutionary multigame with conformists and profiteers based on dynamic complex networks

Evolutionary game on complex networks provides a new research framework for analyzing and predicting group decision-making behavior in an interactive environment, in which most researchers assumed players as profiteers. However, current studies have shown that players are sometimes conformists rather than profit-seeking in society, but most research has been discussed on a simple game without considering the impact of multiple games. In this paper, we study the influence of conformists and profiteers on the evolution of cooperation in multiple games and illustrate two different strategy-updating rules based on these conformists and profiteers. Different from previous studies, we introduce a similarity between players into strategy-updating rules and explore the evolutionary game process, including the strategy updating, the transformation of players' type, and the dynamic evolution of the network structure. In the simulation, we implement our model on scale-free and regular networks and provide some explanations from the perspective of strategy transition, type transition, and network topology properties to prove the validity of our model.

Random growth scale-free networked models with an identical degree distribution and a tunable assortativity index

In this work, we propose two kinds of graphic operations by using triangle configuration, based on which we establish a family of random growth networked models G(t;p) where notations t and p represent time step and probability parameter, respectively. By studying some fundamental structural parameters both analytically and numerically, we show that (1) all the realizations G(t;p) follow the same power-law degree distribution with exponent γ=2+ln⁡3/ln⁡2 regardless of probability p and thus have scale-free feature; (2) each model G(t;p) has a relatively high clustering coefficient; and (3) while network G(t;1) has a small average path length, it is not a unique model possessing small-world property mainly because its diameter D(t;1) does not reach the theoretical lower bound. Next, we make use of assortativity index R to quantify the tendency of forming connection between vertices and observe that (1) model G(t;0) exhibits disassortative mixing because the corresponding index R(t;0) is non-positive, and (2) model G(t;1) is in the opposite direction. As a result, we demonstrate that random model G(t;p) has a tunable quantity R(t;p) controlled by probability p. In addition, we exactly determine the total number of spanning trees of deterministic models G(t;1) and G(t;0) and also calculate the entropy of spanning trees.

Subnormal Distribution Derived From Evolving Networks With Variable Elements

During the past decades, power-law distributions have played a significant role in analyzing the topology of scale-free networks. However, in the observation of degree distributions in practical networks and other nonuniform distributions such as the wealth distribution, we discover that, there exists a peak at the beginning of most real distributions, which cannot be accurately described by a monotonic decreasing power-law distribution. To better describe the real distributions, in this paper, we propose a subnormal distribution derived from evolving networks with variable elements and study its statistical properties for the first time. By utilizing this distribution, we can precisely describe those distributions commonly existing in the real world, e.g., distributions of degree in social networks and personal wealth. Additionally, we fit connectivity in evolving networks and the data observed in the real world by the proposed subnormal distribution, resulting in a better performance of fitness.

Evolving networks based on birth and death process regarding the scale stationarity

Since the past few decades, scale-free networks have played an important role in studying the topologies of systems in the real world. From the traditional perspective, the scale of network, the number of nodes, keeps growing over time without decreasing, leading to the non-stationarity of the scale which is against the real networks. To address this issue, in this paper, we introduce both increase and decrease of vertices to build the evolving network models based on birth and death random processes which are regarded as queuing systems in mathematics. Besides the modeling, the scale of networks based on different random processes is also deduced to be stationary and denoted by a specific probabilistic expression irrelevant to time. In the simulations, we build our network models by different types of queueing systems and compare the statistical results with theories to show the validity and accuracy of our proposed models. Additionally, our model is applied to simulate and predict the populations of some developed countries in recent years.